Understanding Bernoulli's Equation for Fluid Dynamics with Electric Pumps

[mattyboson12]

Hi, am having a few problems applying bernoulli's equation when an electric pump is involved. I have attached a picture of the question. I understand how to apply bernoullis for venturi and pitot tubes but when it involves work being done on the system eg. a water pump, fan exhaust I don't know where to start.

 

[paisiello2]

Can you attempt to answer part a)?

 

[mattyboson12]

Thank you for the reply. This is my answer but I'm not sure if its right as I am getting a negative value for the pump power?

 

[paisiello2]

For part b), you assumed that the difference between the energies at point 1 and 5 is equal to the Work done by the pump. This is correct except the Work is effectively being added to the system at point 1. You incorrectly assumed it is being subtracted from point 1 (or equivalently that it was being added at point 5).

The water coming out at point 5 doesn't really know if there was a pump or if the water level was much higher than that as shown at point 1. So all the energy terms should be additive at point 1 and be set equal to the energy terms at point 5.